Autonomous Categories in Which a ∼ = a * (extended Abstract)

Recently, there has been some interest in autonomous categories (such as compact closed categories) in which the objects are self-dual, in the sense that A = A∗, or even A = A ∗, for all objects A. In this talk, we investigate which coherence conditions should be required of such a category. We also investigate what graphical language could be used to reason about such a category.